Abstract
The time-evolution of scalar fields in the exterior region of black hole spacetimes has received much attention spanning several decades of research. However, the behavior of these fields for the interior region has only relatively recently gained the attention of the research com-munity. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, with special focus on black hole interior. The expected late-time power-law tails on the exterior regions for null infinity, time-like infinity and the horizon are recovered; however, for the interior region, we find that the late-time scalar fields undergo an oscillatory behavior that is characterized by the multipole index ` of the scalar field.